Molecular Dynamics Simulations Indicate that Deoxyhemoglobin,
Oxyhemoglobin, Carboxyhemoglobin, and Glycated Hemoglobin under
Compression and Shear Exhibit an Anisotropic Mechanical Behavior
Sumith Yesudasan, Xianqiao Wang, and Rodney D. Averett*
School of Chemical, Materials, and Biomedical Engineering, College of Engineering, University of Georgia, 597 D.W.
Brooks Drive, Athens, GA 30602
*Corresponding author email: [email protected]
Telephone: 706-542-0863
Abstract We developed a new mechanical model for determining the compression and shear mechanical
behavior of four different hemoglobin structures. Previous studies on hemoglobin structures have focused
primarily on overall mechanical behavior; however, this study investigates the mechanical behavior of
hemoglobin, a major constituent of red blood cells (RBCs), using steered molecular dynamics (SMD)
simulations to obtain anisotropic mechanical behavior under compression and shear loading conditions.
Four different configurations of hemoglobin molecules were considered: deoxyhemoglobin (deoxyHb),
oxyhemoglobin (HbO2), carboxyhemoglobin (HbCO), and glycated hemoglobin (HbA1C). The SMD
simulations were performed on the hemoglobin variants to estimate their unidirectional stiffness and shear
stiffness. Although hemoglobin is structurally denoted as a globular protein due to its spherical shape and
secondary structure, our simulation results show a significant variation in the mechanical strength in
different directions (anisotropy) and also a strength variation among the four different hemoglobin
configurations studied. The glycated hemoglobin molecule possesses an overall higher compressive
mechanical stiffness and shear stiffness when compared to deoxyhemoglobin, oxyhemoglobin, and
carboxyhemoglobin molecules. Further results from the models indicate that the hemoglobin structures
studied possess a soft outer shell and a stiff core based on stiffness.
Keywords
Molecular dynamics, Hemoglobin, Biophysics, Compression, Shear
I. Introduction Understanding the molecular mechanical
properties of thrombi (Weisel, 2004) and their
constituents (Aleman, Walton, Byrnes, & Wolberg,
2014; Lai, Zou, Yang, Yu, & Kizhakkedathu, 2014;
Loiacono et al., 1992; Pretorius & Lipinski, 2013;
van der Spuy & Pretorius, 2013; van Gelder, Nair,
& Dhall, 1996; Wang et al., 2016; Adam R. Wufsus
et al., 2015) is necessary for understanding the bulk
mechanical and physiological function of the
thrombus. Fibrin clots consist mainly of fibrin
(precursor is the molecule fibrinogen), platelets,
and erythrocytes. The mechanical strength of
fibrinogen has been studied in the past years using
experiments (Brown, Litvinov, Discher, & Weisel,
2007; Carlisle et al., 2009; Gottumukkala, Sharma,
& Philip, 1999; McManus et al., 2006; Weisel,
2004), simulations (Gubskaya, Kholodovych,
Knight, Kohn, & Welsh, 2007; Isralewitz, Gao, &
Schulten, 2001; Lim, Lee, Sotomayor, & Schulten,
2008), and multiscale approaches (Govindarajan,
Rakesh, Reifman, & Mitrophanov, 2016;
Perdikaris, Grinberg, & Karniadakis, 2016;
Piebalgs & Xu, 2015). Recent years have witnessed
various experimental studies on the estimation of
the mechanical properties of fibrin clots (Foley,
Butenas, Mann, & Brummel-Ziedins, 2012; Riha,
Wang, Liao, & Stoltz, 1999; Tocantins, 1936;
Weisel, 2004). For example, the estimation of the
Sumith Yesudasan – Molecular Dynamics Simulation of Hemoglobin and its Mechanics
2
mechanical properties of bulk thrombi (Krasokha et
al., 2010) and cross-linked fibrin networks (Weisel,
2004) has been reported. The mechanical behavior
of a single fibrin fiber was also studied (Liu et al.,
2006) by stretching the fibrin fibers using atomic
force microscopy (AFM) tip and fluorescent
microscopy, which reports that the extensibility of
fibrin films is in the range of 100-200% and for
single fibrin fibers it is estimated at 330%. In
addition, the physiological path and functional steps
in fibrin clot formation has been discussed in
numerous research studies (Cito, Mazzeo, &
Badimon, 2013; Undas & Ariëns, 2011; A. Wufsus,
Macera, & Neeves, 2013).
Despite the vast literature in the physiological
understanding and mechanical modeling domain of
fibrin clots, the role of the mechanical strength of
constituents such as RBCs are seldom discussed or
poorly understood from a molecular basis. Thus,
understanding the mechanical properties of the
allosteric protein hemoglobin (a major constituent
of RBCs) is important for the development of
advanced mechanical models of thrombi (clots)
with inclusions (Kamada, Imai, Nakamura,
Ishikawa, & Yamaguchi, 2012; Loiacono et al.,
1992; Mori et al., 2008; Wagner, Steffen, &
Svetina, 2013).
It is well established that RBCs (inclusions of
thrombi) must withstand the increasing pressure of
blood flow and other forces (Svetina, Kuzman,
Waugh, Ziherl, & Žekš, 2004; Teng et al., 2012;
Uyuklu, Meiselman, & Baskurt, 2009; Wu, Guo,
Ma, & Feng, 2015; Yoon & You, 2016), as this may
lead to plastic deformation of the thrombus and
eventually rupture (Weisel, 2004). The focus of
these studies, however, has been primarily at the
continuum level without much focus on molecular
mechanical behavior. Some researchers have
performed investigations on the mechanical and
dynamic behavior of hemoglobin from a molecular
standpoint (Arroyo-Mañez et al., 2011; Kakar,
Hoffman, Storz, Fabian, & Hargrove, 2010;
Koshiyama & Wada, 2011; Xu, Tobi, & Bahar,
2003), and some studies that have been focused on
the molecular mechanical behavior of hemoglobin
variants such as sickled hemoglobin (HbS) (Li, Ha,
& Lykotrafitis, 2012; Li & Lykotrafitis, 2011) and
glycated hemoglobin (De Rosa et al., 1998). There
have also been studies that have addressed the
anisotropic behavior of hemoglobin structures
using fluorescence based methods (Bucci &
Steiner, 1988; Chaudhuri, Chakraborty, &
Sengupta, 2011; Hegde, Sandhya, &
Seetharamappa, 2013; Kantar, Giorgi, Curatola, &
Fiorini, 1992; Plášek, Čermáková, & Jarolím, 1988)
but did not address the molecular mechanical
behavior. In sum, these previous investigations
were limited since they did not explore the
molecular mechanical behavior of hemoglobin (or
its variants) under mechanical compression or shear
loading conditions. Because biological cells (in
particular RBCs) experience compressive and shear
forces physiologically and must exhibit appropriate
transport behavior, an investigation that explores
the molecular anisotropic mechanical behavior of
the comprising proteins under these loading
conditions would be a significant enhancement to
the scientific literature.
In this work, we investigated the mechanical
strength of various forms of hemoglobin, a major
component of RBCs, from an atomistic viewpoint,
utilizing steered molecular dynamics (SMD)
simulations. Four different types of hemoglobin
molecules (deoxyhemoglobin, oxyhemoglobin,
carboxyhemoglobin, and glycated hemoglobin)
were considered to estimate their unidirectional
stiffness and shear stiffness at the molecular level.
The results of this work are important for the
development of advanced cellular mechanical
models in biophysics and bioengineering.
II. Methods
A. Molecular Dynamics Model Hemoglobin (Hb) is a molecule that is considered a globular protein consisting of four
Sumith Yesudasan – Molecular Dynamics Simulation of Hemoglobin and its Mechanics
3
subunits (Fig. 1a). Two of these subunits represent
the chains and the other two represent the
chains. Each of these subunits consists of a heme
group with an iron atom in the center (shown as
bonded molecular representation in Fig. 1a). Here
we consider four different types of Hb molecules,
namely deoxyhemoglobin (RCSB 2DN2),
oxyhemoglobin (RCSB 2DN1),
carboxyhemoglobin (RCSB 2DN3), and glycated
hemoglobin (RCSB 3B75). The deoxyhemoglobin
molecule (deoxyHb) is the form of Hb without any
additional molecules, the oxyhemoglobin molecule
(HbO2) represents the oxygen carrying state of Hb,
and the carboxyhemoglobin molecule (HbCO)
represents the carbon monoxide structure attached
to the Hb molecule. The glycated Hb structure
represents the Hb molecule with bonded glucose
and fructose molecules. These Hb *.pdb models
were solvated in a spherical water volume (Fig. 1b)
and used for molecular compressive and shear
stiffness calculations. The molecular models were
prepared with Visual Molecular Dynamics (VMD)
(Humphrey, Dalke, & Schulten, 1996) and the
molecular dynamics (MD) simulations are
performed with NAMD (Kalé et al., 1999). The
force field employed for the MD simulations was
CHARMM27 (MacKerell, Banavali, & Foloppe,
2000) and the water molecular model used for
solvation was TIP3P (Jorgensen, Chandrasekhar,
Madura, Impey, & Klein, 1983). For equilibration,
an energy minimization was performed for 1,000
steps and then equilibrated using a Langevin
thermostat at 300 K for 10,000 steps followed by an
NVE relaxation for 40,000 steps. This equilibrated
model was used for production runs (compression
studies) with controlled temperature using a
Langevin thermostat (Allen & Tildesley, 1989).
Figure 1. Computational models of human hemoglobin. (a) Deoxyhemoglobin (deoxygenated) in the absence of
solvent. (b) Hb solvated in a sphere.
B. Alignment of models The preliminary molecular models (PDB files)
were arbitrarily oriented in the Cartesian coordinate
system. In order to make reliable comparisons of the
unidirectional stiffness and other mechanical
properties among these four configurations, a
consistent and geometrically similar arrangement of
these four molecular models was necessary. A
geometric basis for all four Hb configurations was
developed using the iron atoms of the heme group,
and they were consistently aligned using a two-step
rotation transformation process (Fig. 2). These
aligned Hb molecule configurations were used for
all SMD analysis studies performed in this work.
Figure 2: Alignment of the Hb molecules. (a) Sample initial orientation of the Hb molecule, with heme group only. A, B, C
and D represent the different subunits and n is the normal vector of triangle ABC. (b) The Hb structure was rotated by aligning
the normal of ABC with the x-axis. (c) The edge AB of the triangle ABC was then aligned with the z-axis. All views of the
molecules shown here are from the xy-plane.
Figure 3: Aligned Hb molecules. The initial and rotated molecular models of hemoglobin are shown for (a-b)
carboxyhemoglobin, (c-d) deoxyhemoglobin, (e-f) oxyhemoglobin and (g-h) glycated hemoglobin, respectively.
The iron atoms of heme of different subunits
were constructed using VMD (A, B, C and D, Fig.
2a). Consider the triangle formed by A, B and C.
Let n be the normal of this triangle ABC. For
consistent orientation arrangement, as a first step
we shifted the Hb molecule by corner A to the
origin and performed a rotation to align normal n
with the x-axis (Fig. 2b). Next, edge AB was
aligned with the z-axis by a single rotation (Fig. 2c).
This translation and rotation procedure was used for
all four Hb molecule variants, namely carboxy,
deoxy, -oxy and glycated hemoglobin (Fig. 3a-b,
Fig. 3c-d, Fig. 3e-f, and Fig. 3g-h, respectively).
Geometric similarity was observed for the aligned
molecules, with the exception of glycated Hb. The
glycated Hb molecule possesses a different internal
Sumith Yesudasan – Molecular Dynamics Simulation of Hemoglobin and its Mechanics
5
structural due to the presence of embedded glucose and fructose molecules.
C. Stiffness Estimation studies In this study, stiffness of the molecule is defined
as the force required for unit deflection. The
unidirectional stiffness was estimated by
compressing the system from either side along the
x, y and z directions. The shear stiffness was
estimated by applying opposing directional
tangential forces on either side of the Hb molecule.
1. Unidirectional stiffness Forces were applied on the peripheral atoms of
the spherically solvated Hb molecule, which mimic
compression using two imaginary rigid plates. A
graphical representation of the force application
strategy is shown in Fig. 4a. Two imaginary rigid
plates move towards the center of the Hb molecule
from both sides. These plates were initially kept at
a distance d0 from the center of the Hb molecule,
which was also the origin of the coordinate system.
During the SMD simulation, the imaginary plates
were moved towards the center at a constant
velocity v. At any instantaneous time (t) from the
beginning of the simulation, the location of the
plates was given as: 0d vt . From this location, a
region of influence was defined at distance rc. A
force (fi) was applied to the 𝑖𝑡ℎ atom which occupies
the region: 0.i cr n d vt r . The applied forces on
atoms are distance dependent and quadratic in
nature, to ensure the Hb molecules were sufficiently
compressed, and to mimic a rigid wall. The force
assumes the form of a quadratic curve initiating
from zero at the point ( 0 cd vt r ) of influence (Fig.
4b), gradually increasing towards the imaginary
plate. The gradient on the plate (Fig. 4a) depicts the
magnitude of the force applied to the molecule,
small near 0 cd vt r and significantly large near
0d vt . The force was applied only to the qualifying
atoms of Hb at every 1 ps. This means, at every 10th
step of time integration, the external force
application is turn on, which simulates a gradual
compression instead of shock force application. A
TCL script in conjunction with NAMD was used to
impose these force criteria onto the system.
Figure 4: Compression strategy for Hb structures. (a) Two imaginary rigid plates travel at a constant velocity towards the
center of the molecule and exerts a variable force on the atoms. The magnitude of the force applied is depicted as the gradient
intensity (red). (b) Applied force vs. distance, where the horizontal axis represents the distance from the origin. The force of
influence in atoms at a particular time t is shown as a shaded diagonal pattern. (c) The atoms occupying the shaded region were
selected and an applied force along the directions was used to simulate shear mechanical behavior.
Sumith Yesudasan – Molecular Dynamics Simulation of Hemoglobin and its Mechanics
6
Utilizing Equations (1) – (2), atoms occupying
the qualifying region ( 0.i cr n d vt r ), were used
to compute and apply the requisite mechanical
forces.
.
.
ii
i
r nf Fn
r n (1)
2
0 0.i cF f r n d vt r (2)
Here, n is the normal vector to the imaginary plates,
ri is the position vector of ith atom, f0 = 100 pN, v =
1 A/ps, and rc = 0.8 nm. This study was difficult to
accomplish in a periodic boundary due to the
pressure fluctuations arising from the localized
density variations and probability of cavitation.
2. Shear stiffness
Shear stiffness is defined as the shear force
required for unit deflection along the shear stress
direction. In the case of shear, estimation of six
shear components corresponding to xy, xz, yx, yz, zx,
and zy, tensor components was necessary. For
example, shear stiffness in the xy direction is
defined asxy xy xyk F d , where kxy is the shear
stiffness, Fxy is the force acting on the shear plane x,
along the y-direction, and dxy is the deflection along
the y-direction. In general, for any shear plane with
unit normal n1, the shear stiffness along unit normal
direction n2 was defined as 1 2 1 2 1 2/kn n Fn n dn n .
The shear force was applied to the atoms of the Hb
molecule using two criteria: 1) an atom selection
was performed based on Equation (3) and 2) the
force on the ith atom was defined by Equation (4).
A graphical explanation of shear force application
and selection of the atoms is described for the case
of shear stiffness calculation in the xy-plane (Fig.
4c).
1 0.i com cr r n d r (3)
10 2
1
.
.
ii
i
r nf f n
r n (4)
Equation (3) is a selection criterion, from which
the qualifying atoms of the Hb molecule within the
influence region of the imaginary rigid surface were
selected and individually applied with a force fi. For
this study analysis: d0 = 3 nm, rc = 1.5 nm, f0 = 100
pN, and rcom is the position vector of the center of
mass of the Hb molecule, which is (0,0,0) in our
case.
III. Results and Discussion
A. Unidirectional Stiffness The rotated and aligned models of hemoglobin
were used to create two molecular models: 1)
spherically solvated model in water and 2) a plain
model in the absence of water (non-solvated). These
two computational models were then used to
compress Hb along the three directions x, y and z
individually using the force application method
explained in the aforementioned. The SMD
simulation was performed for 40 ps, with a time
step of 1 fs, and the compression algorithm was
applied using a TCL script at every 0.01 ps.
Evolutionary mechanical behavior of
deoxyhemoglobin at 10 ps intervals during x-axis
compression (Fig. 5) indicates that 1) the Hb
molecule is compressed tightly into a discoid
structure (front view) 2) experiences a gradual
separation of the subunits (side view), and 3)
experiences separation of the various amino acid
residues (coiled-coil regions).
Figure 5: Uniaxial compression of deoxyhemoglobin molecules. Front view of deoxyHb during compression at (a) initially,
(b) 10 ps, (c) 20 ps and (d) 30 ps. Side view of system under compression at (e) 0 ps, (f) 10 ps, (g) 20 ps, and (h) 30 ps.
Figure 6: Force versus deflection comparison for various
hemoglobin structures: deoxyhemoglobin (deoxyHb),
oxyhemoglobin (HbO2), carboxyhemoglobin (HbCO), and
glycated hemoglobin (HbA1C). The directional forces and
corresponding deflections are shown for (a) x-axis, (b) y-axis,
and (c) z-axis respectively.
The total force applied to the system was
recorded every 1 ps and the deflection was
estimated from the trajectories of the atoms in the
system. The force versus deflection behavior along
all three directions for carboxy, deoxy, -oxy and
glycated hemoglobin molecules is shown in Figs.
6a, 6b, and 6c respectively. The slope estimated
from the curves in Fig. 6 provides the unidirectional
stiffness of Hb molecules.
The slopes (unidirectional stiffness) are shown
in the Fig. 7a for both solvated and non-solvated
cases. The overall trend shows a more rigid
glycated Hb structure compared with the other Hb
variants. In addition, the stiffness along the y-axis
shows almost twice the magnitude in the other two
directions x and z, which reveals an anisotropic
material property of hemoglobin. This anisotropic
mechanical behavior was observed in all Hb
variants.
Sumith Yesudasan – Molecular Dynamics Simulation of Hemoglobin and its Mechanics
8
B. Shear Stiffness The shear force on the Hb molecules was applied
as per the strategy in the aforementioned, for all the
6 possible directions, namely xy, xz, yx, yz, zx, and
zy. MD simulations were performed for every case
with a 10 ps duration and a time integration step of
1 fs. The shear force algorithm was applied using a
TCL script coupled with NAMD, at every 10 fs. The
width of the influence plane used to select atoms
(Fig. 4c) is considered as 1.5 nm on either side.
Figure 7: Stiffness comparison for various hemoglobin variants. (a) Unidirectional stiffness values of deoxy, oxy, carboxy,
and glycated hemoglobin structures are shown for solvated and non-solvated cases. (b) Shear stiffness along XY, XZ, YX, YZ,
ZX and ZY planes for the four hemoglobin variants.
The shear stiffness was estimated for non-
solvated (plain) models (Fig. 7b). In most of the
configurations, the glycated Hb molecule exhibits a
higher shear stiffness. The shear stiffness of the
glycated Hb is much higher than the other Hb
molecules for the cases yx and yz. The shear
stiffness of glycated Hb in the z-plane along y and
x direction shows a lower or equal stiffness as
compared with the other Hb variants, which is
consistent with the unidirectional results.
To verify the sensitivity of the applied force
magnitudes (f0) and compression rate (v), we
performed a set of separate simulations and found
that there is no significant effect on the stiffness
values of Hb. For all three directions (x, y, and z),
the solvated models show higher strength than the
non-solvated models. The results also show an
augmented stiffness of the Hb molecules in the
presence of water as a solvent. The glycated
hemoglobin possesses almost twice the stiffness of
other configurations.
C. Energy Change and RMSD To understand the molecular mechanism and
origin of the stiffness, we have investigated the
various energy contributions and the root mean
square deviation (RMSD) response of the four Hb
molecules during compression. The compressive
strength of the molecule is defined as the ability to
resist deformation, which becomes the ability to
resist the change in potential energy at an atomistic
level. Therefore, the estimation of change in
potential energy during compression may shed light
into the origin of the mechanical strength of the
hemoglobin structures. The energy change of the
hemoglobin systems during compression along the
x, y, and z directions was computed (Fig. 8a, 8b, and
8c respectively). The estimated energy was
averaged with the total number of atoms in the
system (kcal/mol). The energies arising from the
potentials including bond (BOND), angle (ANG),
dihedral (DIHED), improper (IMPR), coulomb
(ELEC), and van der Waals (VDW) were calculated
(Fig. 8). The kinetic energy (KE), total potential
energy (PE) and total energy (TOTAL) was also
computed (Fig. 8).
Figure 8: Energy of the hemoglobin system before and after compression. The energy corresponding to (a) x-axis compression,
(b) y-axis compression, and (c) z-axis compression (1 and 2 correspond to before and after compression, respectively). The
energy is plotted for the four hemoglobin variants.
As displayed in Fig. 8, the results do not show
much variation in the energy before (suffix 1) and
after (suffix 2) compression. The major
contribution to the potential energy was Coulombic
energy and the least contribution was from
improper potential energy. A more in-depth
analysis of the energy change during compression
in terms of percentage change was calculated using:
1 2 1100E E E E (Figure 9). From this
percentage change, the glycated Hb molecule
shows relatively large changes in potential energy
during compression along the x-axis (10%) and y-
axis (24%). When compressed along the z-axis,
there are not considerable variations in energy
across various Hb configurations. These potential
energy changes follow the same trend as the
unidirectional stiffness of the Hb molecules and
hence they are directly related.
Figure 9: Percentage energy change for the four hemoglobin variants in (a) x-direction, (b) y-direction and (c) z-direction. (d)
Percentage change in potential energy for all hemoglobin structures in x, y, and z directions. The variations closely follow the
trend in stiffness property.
Root mean square deviation (RMSD) of the 4
iron atoms present in the heme residues of the
chains and the chains of the Hb molecules during
compression were computed. The RMSD of these
iron atoms while compressing the Hb molecules
along x, y and z directions respectively is displayed
(Fig. 10a, 10b, and 10c). The RMSD was estimated
based on Equation 5. Equation 5 estimates the
RMSD between present and previous states of the
ensemble of atoms, where x, y and z are the
positions of the N atoms, and subscripts i and t
represents i-th atom and time t , and t represents
the time step.
2
( )
2
( )
12
( )
it i t t
N
it i t t
i
it i t t
x x
RMSD y y N
z z
(5)
The maximum RMSD of the iron atoms for all the
cases was also calculated (Fig. 10d).
Figure 10: RMSD evolution of Fe atoms of heme residue for first 20 ps during (a) x-direction compression, (b) y-direction
compression, and (c) z-direction compression. The slope of this RMSD curve was estimated for (e) initial 3 ps and (f) final 3
ps and plotted. This shows the rate of compression. (d) The final RMSD of the hemoglobins in all directions are shown.
The trend of the RMSD shows a linear slope in
the beginning of the compression (0 ps to 5 ps) and
a steep nonlinear mechanical behavior towards the
end of compression (15 ps to 20 ps) (Fig. 10a-c).
These slopes were evaluated separately (Fig. 10e
and 10f). The RMSD slope mathematically
correlates to the expansion rate of the Fe atoms, and
increases by a factor of 6 towards the end of
compression. Since the RMSD is dependent on the
atomic coordinates on all three directions x, y and z,
the results in Fig. 10 show that the Fe atoms
approach one another during compression along the
loading axis at the initiation. When the Hb
molecules compress and flatten like an oval disc
(Figs. 5d and 5h), these Fe atoms separate
perpendicular to the compression axis. This also
shows that the core molecules in the heme residue
actively participate in the structural activity after
the ‘shell’ or peripheral molecules become
compressed.
D. Solvation Volume Sensitivity and Hydrogen Bonds A cutoff potential of 1 nm was used for all MD
simulations in this work with a water solvation
volume of 1.5 nm thickness surrounding the Hb
molecules. The effects of larger solvation spheres
on stiffness calculations are seldom due to the non-
periodic boundary condition or the short-range
potential cutoff of 1 nm.
Figure 11. Sensitivity study of solvation volume influence on stiffness of the Hb molecule. Solvated models of hemoglobin
with water envelope of (a) 1.5 nm, (b) 3 nm, (c) 4.5 nm and (d) 6 nm. (e) Force vs. deflection graph for x-direction compression
for oxyhemoglobin with different solvation volumes, where r is the radius of the Hb molecule.
To corroborate this non-sensitivity, we solvated
the Hb molecules in various spheres ranging from
1.5 nm to 6 nm envelopes (Fig. 11a-d). The
deflection of the Hb molecules was then computed
by applying compressive forces along the x-
direction. The compression results (Fig. 11e) do not
display any influence of bigger solvation spheres.
To understand the possible role of hydrogen
bonds (H-bonds) on the stiffness of the Hb
molecules, the number of bonds formed was
calculated during the compression process using
VMD (Humphrey et al., 1996). Figure 12 shows the
number of hydrogen bonds formed between Hb
molecules and water during the compression
process for the various Hb molecules along
different directions. For all four Hb variants, the
calculations show no change in the number of
hydrogen bonds formed. Subsequent to 15 ps, there
is a steady decline in the number of hydrogen bonds
and this is correlated with the RMSD results (Fig.
10a-c), where a steady compression is observed
Sumith Yesudasan – Molecular Dynamics Simulation of Hemoglobin and its Mechanics
13
after 15 ps. These results indicate that hydrogen
bonds contribute significantly to Hb compressive
stiffness, and in particular explain the augmented
stiffness in the solvated case.
Figure 12: Evolution of the number of hydrogen bonds formed during compression along (a) x-axis compression, (b) y-axis
compression and (c) z-axis compression.
IV. Conclusions In this paper, we have investigated the
mechanical properties of various forms of
hemoglobin in different physiological states.
Unidirectional stiffness and shear stiffness were
calculated for deoxyhemoglobin (deoxyHb),
oxyhemoglobin (HbO2), carboxyhemoglobin
(HbCO), and glycated hemoglobin (HbA1C). The
unidirectional stiffness varied significantly among
these four configurations, where the glycated Hb
displayed the highest stiffness compared to the
other three hemoglobin variants. With respect to
shear stiffness, the results show a similar trend to
that of unidirectional stiffness with glycated Hb
displaying the highest shear strength. Although the
Hb molecule has been classified as a globular
protein due to its chemical composition, from our
structural analysis, the Hb molecule demonstrates a
strikingly anisotropic stiffness behavior as
evidenced by its strength in one direction twice
larger than the other two directions. We have
estimated the different components of the potential
energy change during compression and observed
that the Coulombic interaction is the main energy
component responsible for the material stiffness of
hemoglobin. The RMSD results pertaining to the
Hb molecules under compression indicate that the
active participation of the heme protein evolves
later in the process, and clearly shows that
hemoglobin possesses a soft shell and a rigid core.
Thus, from a mechanical behavior standpoint, we
conclude that hemoglobin is an anisotropic material
with a stiff core and a contiguous soft shell. From
our solvated studies and hydrogen bond analysis,
we have found that the hemoglobin molecules
possess additional strength by creating hydrogen
bonds in the presence of water. The mechanical
models that were developed in this study can be
utilized to develop mesoscopic models that can be
employed in multiscale simulations. This study can
serve as a basis for the multiscale model
development of erythrocytes, and is expected to
provide insights on the development of mechanical
models of erythrocytes in the area of thrombosis
and hemostasis.
Sumith Yesudasan – Molecular Dynamics Simulation of Hemoglobin and its Mechanics
14
Acknowledgements Research reported in this publication was
supported by the National Heart, Lung, and Blood
Institute of the National Institutes of Health under
Award Number K01HL115486. The content is
solely the responsibility of the authors and does not
necessarily represent the official views of the
National Institutes of Health. This study was also
supported in part by resources and technical
expertise from the Georgia Advanced Computing
Resource Center, a partnership between the
University of Georgia’s Office of the Vice
President for Research and Office of the Vice
President for Information Technology.
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